Experimental set up
A compound channel setup was used for this case study. The paper
including all information about the experience was found in Dupuis et al. (2017).
- Length: 18 m
- Width: 3 m
- Slope: 0.00105
- Main channel: 1 m wide rectangular glass bed
- Floodplain: two 1 m wide rectangular configuration. Both floodplains
were covered either by plastic grass alone (meadow) or by an array of
emergent cylinders set on the plastic grass (wood).
- Vertical distance from the main channel to the floodplain: 0.115
m
- Flow conditions: uniform flow with a total discharge of 162 L/s,
varying the discharge in the floodplain of 12 and 18 L/s.
- Water level measurements: the measures were taken spatial
distributed from 2 m to 17 m.


Objectives and remarks of the case study
- Test the estimation when the friction in the floodplain changes
suddenly in longitudinal direction
- Estimate a constant friction in the main channel and a linear
combination in the floodplain
Calibration data
A sample was taken of all measurements for this case.
| 1 |
1 |
2.225 |
3420 |
0.1949608 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
4.310 |
3420 |
0.1880788 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.270 |
3420 |
0.1852095 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.240 |
3420 |
0.1829345 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
8.315 |
3420 |
0.1767361 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.115 |
3420 |
0.1744950 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.250 |
3420 |
0.1744835 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
10.250 |
3420 |
0.1737731 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.250 |
3420 |
0.1732561 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.250 |
3420 |
0.1728932 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.250 |
3420 |
0.1729610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.225 |
3420 |
0.1902885 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.975 |
3420 |
0.1911852 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
3.345 |
3420 |
0.1892610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
4.095 |
3420 |
0.1882043 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
5.060 |
3420 |
0.1864261 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.240 |
3420 |
0.1797323 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.990 |
3420 |
0.1818093 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.030 |
3420 |
0.1790497 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.795 |
3420 |
0.1743624 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.065 |
3420 |
0.1760431 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.115 |
3420 |
0.1721755 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.545 |
3420 |
0.1748087 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
10.030 |
3420 |
0.1738211 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
11.370 |
3420 |
0.1701349 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.120 |
3420 |
0.1723571 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.325 |
3420 |
0.1718688 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
13.290 |
3420 |
0.1715232 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |

Estimation: constant in the main channel and the floodplain (n_kmin
= 0 and n_kflood = 2)
Check MCMC


Partial conclusions:
MCMC unstabilities are observed for all the parameters. Non
convergence has been atteint during the estimation.
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in L/s and velocity in mm/s.
| N |
5.62600e+03 |
5626.00000 |
5626.00000 |
5626.00000 |
5.62600e+03 |
5626.000000 |
5626.000000 |
5626.000000 |
5626.000000 |
| Minimum |
3.55184e+01 |
0.23387 |
-1649.16000 |
-361.31500 |
5.00000e-07 |
5.409260 |
4.733140 |
4.586530 |
4.809350 |
| Maximum |
3.80910e+03 |
1316.18000 |
529.62900 |
726.81500 |
1.90994e-02 |
21.342000 |
19.417600 |
26.271400 |
19.035800 |
| Range |
3.77358e+03 |
1315.95000 |
2178.79000 |
1088.13000 |
1.90989e-02 |
15.932700 |
14.684500 |
21.684900 |
14.226400 |
| Mean |
3.80925e+02 |
215.93000 |
-74.06050 |
59.93410 |
3.64720e-03 |
10.200500 |
10.197200 |
10.006100 |
10.231800 |
| Median |
8.95089e+01 |
144.77400 |
1.12262 |
5.65817 |
3.02540e-03 |
9.996930 |
9.997970 |
9.834780 |
10.058500 |
| Q10% |
5.52200e+01 |
26.66660 |
-693.56600 |
-85.22800 |
6.35200e-04 |
7.735390 |
7.683250 |
7.567800 |
7.731010 |
| Q25% |
6.64882e+01 |
63.29960 |
-19.95560 |
-6.18817 |
1.55030e-03 |
8.795520 |
8.674330 |
8.630330 |
8.776950 |
| Q75% |
2.00965e+02 |
263.03100 |
117.53100 |
89.93690 |
5.09150e-03 |
11.421300 |
11.455500 |
11.210800 |
11.522900 |
| Q90% |
1.48642e+03 |
499.93300 |
331.60000 |
299.15600 |
7.51320e-03 |
12.853500 |
13.116400 |
12.572400 |
12.881300 |
| St.Dev. |
6.77711e+02 |
232.48200 |
395.88900 |
172.34800 |
2.75550e-03 |
2.028350 |
2.146470 |
2.064640 |
2.015110 |
| Variance |
4.59292e+05 |
54047.90000 |
156728.00000 |
29703.90000 |
7.60000e-06 |
4.114190 |
4.607330 |
4.262730 |
4.060650 |
| CV |
1.77912e+00 |
1.07665 |
5.34548 |
2.87563 |
7.55499e-01 |
0.198848 |
0.210495 |
0.206337 |
0.196945 |
| Skewness |
2.45334e+00 |
2.04403 |
-1.71270 |
1.17837 |
1.13990e+00 |
0.696739 |
0.655586 |
0.852583 |
0.556058 |
| Kurtosis |
5.13545e+00 |
4.22783 |
2.76191 |
2.19167 |
1.44975e+00 |
1.163800 |
0.541119 |
2.926970 |
0.319571 |
| MaxPost |
1.64516e+02 |
9.47946 |
5.31925 |
5.32603 |
1.80120e-03 |
9.848100 |
9.865230 |
9.204450 |
9.287330 |
| St.Dev. |
677.711 |
232.48200 |
395.88900 |
172.34800 |
2.75547 |
2028.35 |
214.647 |
2.06464 |
2.01511 |
| MaxPost |
164.516 |
9.47946 |
5.31925 |
5.32603 |
1.80125 |
9848.10 |
986.523 |
9.20445 |
9.28733 |
Check spatial friction distribution


Partial conclusions:
- The estimated values are not coherent.
Check of residuals
| 1 |
1 |
2.225 |
3420 |
0.1949608 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
4.310 |
3420 |
0.1880788 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.270 |
3420 |
0.1852095 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.240 |
3420 |
0.1829345 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
8.315 |
3420 |
0.1767361 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.115 |
3420 |
0.1744950 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.250 |
3420 |
0.1744835 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
10.250 |
3420 |
0.1737731 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.250 |
3420 |
0.1732561 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.250 |
3420 |
0.1728932 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.250 |
3420 |
0.1729610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.225 |
3420 |
0.1902885 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.975 |
3420 |
0.1911852 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
3.345 |
3420 |
0.1892610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
4.095 |
3420 |
0.1882043 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
5.060 |
3420 |
0.1864261 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.240 |
3420 |
0.1797323 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.990 |
3420 |
0.1818093 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.030 |
3420 |
0.1790497 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.795 |
3420 |
0.1743624 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.065 |
3420 |
0.1760431 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.115 |
3420 |
0.1721755 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.545 |
3420 |
0.1748087 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
10.030 |
3420 |
0.1738211 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
11.370 |
3420 |
0.1701349 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.120 |
3420 |
0.1723571 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.325 |
3420 |
0.1718688 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
13.290 |
3420 |
0.1715232 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |


Partial conclusions:
All simulations of MAP estimation are passing through the observed
data with their uncertainty.
Estimation (n_kmin = 0 and n_kflood = 2, with lower
uncertainty)
Check MCMC


Partial conclusions:
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in L/s and velocity in mm/s.
| N |
5.62600e+03 |
5626.000000 |
5626.000000 |
5626.0000000 |
5.62600e+03 |
5626.000000 |
5626.000000 |
5626.000000 |
5626.000000 |
| Minimum |
6.75107e+01 |
6.469160 |
-906.062000 |
-0.7573170 |
2.20000e-06 |
4.691900 |
5.153310 |
4.907100 |
5.132820 |
| Maximum |
3.76359e+03 |
623.575000 |
3.415800 |
445.0820000 |
8.49710e-03 |
19.618200 |
22.568900 |
19.288500 |
19.072600 |
| Range |
3.69608e+03 |
617.106000 |
909.478000 |
445.8390000 |
8.49490e-03 |
14.926300 |
17.415600 |
14.381400 |
13.939800 |
| Mean |
7.08821e+02 |
184.403000 |
-254.284000 |
112.8090000 |
1.45270e-03 |
10.241000 |
10.269800 |
10.210000 |
10.273000 |
| Median |
4.43296e+02 |
127.911000 |
-184.112000 |
91.1873000 |
1.14500e-03 |
10.045800 |
10.006700 |
10.031300 |
10.114900 |
| Q10% |
1.13531e+02 |
30.370700 |
-592.779000 |
10.0411000 |
2.22500e-04 |
7.826580 |
7.763490 |
7.726840 |
7.853240 |
| Q25% |
1.43163e+02 |
53.332800 |
-449.539000 |
24.8515000 |
5.47400e-04 |
8.830190 |
8.689880 |
8.720070 |
8.844560 |
| Q75% |
1.09482e+03 |
299.779000 |
-22.523900 |
184.4360000 |
2.12150e-03 |
11.473300 |
11.474700 |
11.395800 |
11.502200 |
| Q90% |
1.77611e+03 |
407.080000 |
-9.443910 |
238.5600000 |
3.06040e-03 |
12.887600 |
13.060000 |
13.022800 |
12.874700 |
| St.Dev. |
6.92355e+02 |
145.974000 |
239.004000 |
94.9262000 |
1.16140e-03 |
2.048740 |
2.193510 |
2.120600 |
2.023380 |
| Variance |
4.79356e+05 |
21308.300000 |
57123.100000 |
9010.9800000 |
1.30000e-06 |
4.197320 |
4.811480 |
4.496930 |
4.094050 |
| CV |
9.76770e-01 |
0.791603 |
0.939910 |
0.8414740 |
7.99460e-01 |
0.200052 |
0.213588 |
0.207697 |
0.196961 |
| Skewness |
1.20876e+00 |
0.677851 |
-0.617061 |
0.7780830 |
1.22652e+00 |
0.590819 |
0.874968 |
0.665839 |
0.605191 |
| Kurtosis |
8.19305e-01 |
-0.728789 |
-0.798636 |
-0.0533204 |
1.91539e+00 |
0.533511 |
1.382410 |
0.667490 |
0.521433 |
| MaxPost |
1.30432e+02 |
31.930300 |
-10.834200 |
22.9262000 |
3.75100e-04 |
9.156150 |
9.644310 |
9.403030 |
10.409300 |
| St.Dev. |
692.355 |
145.9740 |
239.0040 |
94.9262 |
1.161410 |
2048.74 |
219.351 |
2.12060 |
2.02338 |
| MaxPost |
130.432 |
31.9303 |
-10.8342 |
22.9262 |
0.375124 |
9156.15 |
964.431 |
9.40303 |
10.40930 |
Check spatial friction distribution


Partial conclusions:
Check of residuals
| 1 |
1 |
2.225 |
3420 |
0.1949608 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
4.310 |
3420 |
0.1880788 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.270 |
3420 |
0.1852095 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.240 |
3420 |
0.1829345 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
8.315 |
3420 |
0.1767361 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.115 |
3420 |
0.1744950 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.250 |
3420 |
0.1744835 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
10.250 |
3420 |
0.1737731 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.250 |
3420 |
0.1732561 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.250 |
3420 |
0.1728932 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.250 |
3420 |
0.1729610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.225 |
3420 |
0.1902885 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.975 |
3420 |
0.1911852 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
3.345 |
3420 |
0.1892610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
4.095 |
3420 |
0.1882043 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
5.060 |
3420 |
0.1864261 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.240 |
3420 |
0.1797323 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.990 |
3420 |
0.1818093 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.030 |
3420 |
0.1790497 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.795 |
3420 |
0.1743624 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.065 |
3420 |
0.1760431 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.115 |
3420 |
0.1721755 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.545 |
3420 |
0.1748087 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
10.030 |
3420 |
0.1738211 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
11.370 |
3420 |
0.1701349 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.120 |
3420 |
0.1723571 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.325 |
3420 |
0.1718688 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
13.290 |
3420 |
0.1715232 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |


Partial conclusions:
Estimation (n_kmin = 0 and n_kflood = 4)
Check MCMC


Partial conclusions:
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in L/s and velocity in mm/s.
| N |
5626.00000 |
5626.000000 |
5626.000000 |
5626.000000 |
5626.000000 |
5.62600e+03 |
5.62600e+03 |
5626.000000 |
5626.000000 |
5626.000000 |
5.62600e+03 |
| Minimum |
34.08810 |
0.149982 |
-714.229000 |
-876.929000 |
-1115.750000 |
-1.13655e+03 |
6.40000e-06 |
5.188060 |
4.875490 |
4.787370 |
4.66734e+00 |
| Maximum |
1595.27000 |
329.581000 |
509.053000 |
1014.560000 |
816.162000 |
5.64543e+02 |
2.15719e-02 |
19.807000 |
20.685000 |
20.019600 |
1.98484e+01 |
| Range |
1561.18000 |
329.431000 |
1223.280000 |
1891.490000 |
1931.910000 |
1.70109e+03 |
2.15655e-02 |
14.618900 |
15.809500 |
15.232200 |
1.51811e+01 |
| Mean |
175.29700 |
111.279000 |
-50.114700 |
-60.414800 |
45.204000 |
-2.23995e+02 |
3.63140e-03 |
10.297300 |
10.188900 |
10.109100 |
1.01979e+01 |
| Median |
89.50410 |
97.248900 |
-19.822600 |
0.853679 |
25.665100 |
-1.41474e+02 |
3.02560e-03 |
10.109100 |
9.968710 |
9.925880 |
1.00470e+01 |
| Q10% |
62.75600 |
18.091100 |
-240.079000 |
-374.045000 |
-137.345000 |
-6.56785e+02 |
5.69800e-04 |
7.858830 |
7.866260 |
7.645040 |
7.61636e+00 |
| Q25% |
71.81740 |
46.431600 |
-87.710600 |
-93.929900 |
0.527044 |
-3.93629e+02 |
1.45400e-03 |
8.847970 |
8.764370 |
8.636070 |
8.63273e+00 |
| Q75% |
159.00300 |
173.235000 |
-1.037850 |
19.015900 |
145.817000 |
-1.45462e+01 |
5.18570e-03 |
11.494700 |
11.417100 |
11.365800 |
1.15893e+01 |
| Q90% |
417.13300 |
219.720000 |
115.779000 |
44.899300 |
325.875000 |
-4.82369e-01 |
7.55810e-03 |
12.979000 |
12.883400 |
12.771200 |
1.30527e+01 |
| St.Dev. |
218.22500 |
75.380200 |
155.191000 |
216.661000 |
262.940000 |
2.74926e+02 |
2.79570e-03 |
2.040720 |
2.027860 |
2.053500 |
2.07258e+00 |
| Variance |
47622.10000 |
5682.170000 |
24084.300000 |
46942.100000 |
69137.700000 |
7.55842e+04 |
7.80000e-06 |
4.164530 |
4.112220 |
4.216860 |
4.29559e+00 |
| CV |
1.24488 |
0.677396 |
3.096720 |
3.586230 |
5.816750 |
1.22737e+00 |
7.69879e-01 |
0.198180 |
0.199027 |
0.203133 |
2.03236e-01 |
| Skewness |
2.94893 |
0.436424 |
-0.574716 |
-0.441637 |
-1.354490 |
-6.06785e-01 |
1.13053e+00 |
0.571616 |
0.624735 |
0.576387 |
4.21090e-01 |
| Kurtosis |
9.09418 |
-0.794598 |
2.669210 |
4.755250 |
4.643280 |
7.06489e-02 |
1.62841e+00 |
0.643217 |
0.804943 |
0.626208 |
8.73986e-02 |
| MaxPost |
250.65500 |
2.591520 |
2.466420 |
0.405612 |
2.052370 |
-3.72801e+00 |
1.48080e-03 |
9.550830 |
9.965600 |
10.677200 |
9.51736e+00 |
| St.Dev. |
218.225 |
75.38020 |
155.19100 |
216.661000 |
262.94000 |
274.92600 |
2.79574 |
2040.72 |
202.786 |
2.0535 |
2.07258 |
| MaxPost |
250.655 |
2.59152 |
2.46642 |
0.405612 |
2.05237 |
-3.72801 |
1.48076 |
9550.83 |
996.560 |
10.6772 |
9.51736 |
Check spatial friction distribution


Partial conclusions:
Check of residuals
| 1 |
1 |
2.225 |
3420 |
0.1949608 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
4.310 |
3420 |
0.1880788 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.270 |
3420 |
0.1852095 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.240 |
3420 |
0.1829345 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
8.315 |
3420 |
0.1767361 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.115 |
3420 |
0.1744950 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.250 |
3420 |
0.1744835 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
10.250 |
3420 |
0.1737731 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.250 |
3420 |
0.1732561 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.250 |
3420 |
0.1728932 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.250 |
3420 |
0.1729610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.225 |
3420 |
0.1902885 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.975 |
3420 |
0.1911852 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
3.345 |
3420 |
0.1892610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
4.095 |
3420 |
0.1882043 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
5.060 |
3420 |
0.1864261 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.240 |
3420 |
0.1797323 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.990 |
3420 |
0.1818093 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.030 |
3420 |
0.1790497 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.795 |
3420 |
0.1743624 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.065 |
3420 |
0.1760431 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.115 |
3420 |
0.1721755 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.545 |
3420 |
0.1748087 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
10.030 |
3420 |
0.1738211 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
11.370 |
3420 |
0.1701349 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.120 |
3420 |
0.1723571 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.325 |
3420 |
0.1718688 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
13.290 |
3420 |
0.1715232 |
-9999 |
-9999 |
-9999 |
-9999 |
0.0222257 |
-9999 |
-9999 |
-9999 |
-9999 |


Estimation (n_kmin = 0 and n_kflood = 4, with lower
uncertainty)
Check MCMC


Partial conclusions:
Check summary
Zoom into the MAP and standard deviation of the error model:
WSE in mm, discharge in L/s and velocity in mm/s.
| N |
5626.000000 |
5626.000000 |
5.62600e+03 |
5626.000000 |
5626.00000 |
5626.000000 |
5.62600e+03 |
5626.000000 |
5626.000000 |
5626.000000 |
5626.000000 |
| Minimum |
45.384900 |
0.645952 |
-1.12552e+02 |
-820.216000 |
-711.74200 |
-996.927000 |
1.10000e-06 |
5.251240 |
5.355910 |
4.872830 |
4.401990 |
| Maximum |
269.872000 |
338.195000 |
6.88412e+02 |
398.163000 |
665.78300 |
719.385000 |
6.56170e-03 |
20.015800 |
21.821500 |
22.341300 |
18.295500 |
| Range |
224.487000 |
337.549000 |
8.00964e+02 |
1218.380000 |
1377.53000 |
1716.310000 |
6.56070e-03 |
14.764600 |
16.465600 |
17.468500 |
13.893500 |
| Mean |
101.143000 |
100.198000 |
1.07237e+02 |
73.911700 |
-60.51250 |
24.161000 |
1.38490e-03 |
10.197400 |
10.253100 |
10.291300 |
10.179400 |
| Median |
76.734600 |
70.955500 |
1.63633e+00 |
34.127000 |
1.29157 |
-0.556933 |
1.12060e-03 |
10.064100 |
10.061700 |
10.078900 |
10.010700 |
| Q10% |
58.998400 |
13.520600 |
-4.93987e+01 |
-30.213800 |
-342.17100 |
-93.134000 |
2.24300e-04 |
7.784890 |
7.762610 |
7.793300 |
7.639570 |
| Q25% |
66.375400 |
28.300500 |
-2.37196e+01 |
7.815460 |
-147.22500 |
-26.030400 |
5.03100e-04 |
8.733890 |
8.732530 |
8.860140 |
8.678860 |
| Q75% |
140.167000 |
160.082000 |
2.09499e+02 |
170.057000 |
22.65480 |
67.397200 |
2.01190e-03 |
11.431000 |
11.502300 |
11.531100 |
11.490200 |
| Q90% |
175.526000 |
240.423000 |
4.19283e+02 |
262.329000 |
105.22600 |
189.517000 |
3.04640e-03 |
12.837100 |
12.972500 |
13.068300 |
12.990700 |
| St.Dev. |
47.770500 |
85.409700 |
1.83531e+02 |
131.113000 |
176.85200 |
154.292000 |
1.10360e-03 |
2.023590 |
2.098270 |
2.054680 |
2.089490 |
| Variance |
2282.020000 |
7294.820000 |
3.36837e+04 |
17190.700000 |
31276.60000 |
23806.000000 |
1.20000e-06 |
4.094930 |
4.402740 |
4.221700 |
4.365960 |
| CV |
0.472307 |
0.852407 |
1.71145e+00 |
1.773920 |
2.92257 |
6.385980 |
7.96907e-01 |
0.198441 |
0.204647 |
0.199652 |
0.205266 |
| Skewness |
1.049390 |
0.806604 |
1.10736e+00 |
-0.576183 |
-1.03814 |
-0.184789 |
1.10553e+00 |
0.595984 |
0.697967 |
0.561048 |
0.507925 |
| Kurtosis |
-0.099795 |
-0.542128 |
-3.90113e-02 |
3.452190 |
1.09225 |
9.423940 |
1.12833e+00 |
0.706034 |
0.994271 |
0.525864 |
0.260188 |
| MaxPost |
188.472000 |
31.866300 |
-3.01994e+01 |
26.820700 |
-5.81556 |
1.553310 |
2.54800e-04 |
8.733280 |
9.245970 |
9.449770 |
10.113700 |
| St.Dev. |
47.7705 |
85.4097 |
183.5310 |
131.1130 |
176.85200 |
154.29200 |
1.103620 |
2023.59 |
209.827 |
2.05468 |
2.08949 |
| MaxPost |
188.4720 |
31.8663 |
-30.1994 |
26.8207 |
-5.81556 |
1.55331 |
0.254818 |
8733.28 |
924.597 |
9.44977 |
10.11370 |
Check spatial friction distribution


Partial conclusions:
Check of residuals
| 1 |
1 |
2.225 |
3420 |
0.1949608 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
4.310 |
3420 |
0.1880788 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
5.270 |
3420 |
0.1852095 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
6.240 |
3420 |
0.1829345 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
8.315 |
3420 |
0.1767361 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.115 |
3420 |
0.1744950 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
9.250 |
3420 |
0.1744835 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
10.250 |
3420 |
0.1737731 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
11.250 |
3420 |
0.1732561 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
12.250 |
3420 |
0.1728932 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 1 |
1 |
13.250 |
3420 |
0.1729610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.225 |
3420 |
0.1902885 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
2.975 |
3420 |
0.1911852 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
3.345 |
3420 |
0.1892610 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
4.095 |
3420 |
0.1882043 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
5.060 |
3420 |
0.1864261 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.240 |
3420 |
0.1797323 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
6.990 |
3420 |
0.1818093 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.030 |
3420 |
0.1790497 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
8.795 |
3420 |
0.1743624 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.065 |
3420 |
0.1760431 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.115 |
3420 |
0.1721755 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
9.545 |
3420 |
0.1748087 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
10.030 |
3420 |
0.1738211 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
11.370 |
3420 |
0.1701349 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.120 |
3420 |
0.1723571 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
12.325 |
3420 |
0.1718688 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |
| 2 |
1 |
13.290 |
3420 |
0.1715232 |
-9999 |
-9999 |
-9999 |
-9999 |
0.008 |
-9999 |
-9999 |
-9999 |
-9999 |


Main conclusions:
- Thee streamwise distance as covariant to spatial distribute the
friction coefficient is not enough to estimate the friction coefficient
when the roughness changes suddenly. Changes are modelized smoothly, but
the real-world conditions are not.
- However, this example allows to prove that the methodology is able
to estimate constant friction using a picewise function (to be
tested)
Bibliography:
Dupuis, Victor, Sébastien Proust, Céline Berni, and André Paquier. 2017.
“Compound Channel Flow with a Longitudinal Transition in Hydraulic
Roughness over the Floodplains.” Environmental Fluid
Mechanics 17 (5): 903–28.
https://doi.org/10.1007/s10652-017-9525-0.